496 APPLIED MECHANICS 
Wheel Speed.—Assuming 0,=90°, it has been shown that 
’ 
pile a Pe: o: e008 , therefore c ea gi: cos pK, ./2gh= ) 
1 1 2 1 ethy a! ae 
Ag 1 Ag 1g 
E 
A,” Avir 
where ba has : =F oy 2a, : i . cos 4, cos dy 
= f _E.. ; AY cos dy may be called the coefficient of wheel speed. 
2cos@, Ag 1 we 
If instead of assuming 0.=90° it be assumed that w)=ca, then it 
7 
follows that K, = Bd (3 3 “\ cos 6, + cos dy — 1). 
2 a 
Effective or Brake Horse-power =. 
430. Use of Suction Tube for Reaction Turbines.—Since a 
turbine works full of water, it is not necessary that it should be placed” 
at the level of the tail water in order to utilise the full head. A ion. 
turbine may with advantage be placed at a height, less than the height 
of the water barometer, above the tail water, provided that it discha 
into a pipe which, running full, opens under the tail water. The ady 
tages of this arrangement are that a shorter shaft is necessary, and 
turbine is more accessible. 
Exercises XXIX. 
1. The effective horse-power of a vertical water wheel is 28, and its efficiency — 
is 70 per cent. If the total fall is 20 feet, how many gallons of water must be 
delivered to the wheel per minute ? i 
2. The head race of a vertical water wheel is 5 feet wide, and the water in 
it is 6 inches deep, and has a velocity of 10 feet per second. ‘The total fall is — 
30 feet, and the efficiency of the wheel is 75 per cent. What is the effective — 
horse-power of the wheel ? y 
3. The stream impinging on the vanes of a common undershot water wheel — 
passes through a sluice opening 6 inches deep and 5 feet wide. The head of 
water is 4 feet 6 inches. Taking the coefficient of discharge for the sluice 
opening at 0°62, and the efficiency at 30 per cent., what is the useful horse-— 
power of the wheel ? q 
4. If in a Poncelet wheel the water enters in a direction bisecting 
angle @ between the tangents to the wheel and vane at the tip of the latte 
and if the points of entrance and exit are at the same level, show that, so far 
as the action of the water on the vanes is concerned, the efficiency is equal to 
1 — tan? > the friction of the water on the vanes being neglected. . ‘ 
5. The centres of the buckets of a Pelton wheel move ina circle 3 feet i 
diameter. The actual head of water for the jet is 2000 feet, and the diamet« 
of the jet is } inch. The wheel makes 1000 revolutions per minute, and develops — 
80 horse-power, using 28 cubic feet of water per minute. Determine, (a) the 
resultant efficiency, (b) the loss of head estimated at the jet, and (c) the 
of the mean velocity of the buckets to the actual velocity of the jet. 
